The present invention pertains to an apparatus for and a method of determining an approximation of the envelope of a complex baseband signal having an in-phase component I and a quadrature component Q. More particularly, the present invention pertains to an apparatus for and a method of determining such envelope in a computationally efficient manner, permitting implementation in a gate array to provide high speed operation.
In digital radio, it is desirable to be able to compute the envelope of the baseband signal with minimal distortion. When transmitting a modulated radio signal, it is desirable to maintain out of band emissions at an extremely low level by minimizing the distortion in the output of the power amplifier. When demodulating a received amplitude modulated signal, it is also desirable to minimize the distortion in the envelope computation. In order to accomplish these, it is necessary to accurately and rapidly compute the envelope of the modulated signal. The envelope comprises two components; namely, an in-phase component I and a quadrature component Q. Determination of the envelope can readily be achieved by determining the square root of the sum of the squares of I and Q for each value of I and Q.
In embedded real time digital implementations, determination of the square root of a complex signal requires a significant number of clock cycles utilizing software, or a significant number of logic blocks utilizing firmware. It is desirable to minimize the number of clock cycles or logic blocks required. To achieve envelope predistortion required for linear transmission of differential eight phase shift keying (D8PSK) waveforms, such as required by International Civil Aviation Organization Mode 2 specifications, the envelope must be computed as accurately as possible so as to avoid spectral spurs. A common approximation of the square root is obtained by adding the maximum of the absolute values of I or Q to three-eighths the minimum values of I or Q. However, this approximation is not sufficiently accurate for use in transmit envelope predistortion, particularly when the values of I and Q are almost equal. While look-up tables could be used, a different look-up table would be required for each power level, requiring a significant amount of memory. It is desirable to determine the square root in a gate array, so as to obtain the resulting advantage of high speed. However, gate arrays are not practical for the large number of look-up tables required because of their limited memory.
The present invention is an apparatus for and a method of determining the envelope of a complex baseband signal having an in-phase component I and a quadrature component Q. In accordance with the present invention, the square root of the sum of the squares of the values of I and Q is determined as a value of the envelope. A polynomial representation of the square root, which deviates only slightly from a true square root polynomial, is utilized. In one embodiment of the present invention, a simplified alternating series polynomial, in the form of a sixth-order polynomial with unity coefficients, is used to approximate the square root. A second embodiment of the invention utilizes a ratio of two polynomials to provide a somewhat less accurate, but still usable, approximation of the square root. Preferably, the apparatus is implemented in a gate array.